Binding energy of neutral bound excitons in GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells

The binding energy of an exciton bound to a neutral donor (${\mathrm{D}}^0$,X) in a GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum well is calculated variationally by using a two-parameter wave function. There is no artificial parameter added in our calculation. Our results agree fairly well with previous experimental results, except that our position of the binding energy maximum is at about 15 Å, not at 100 Å as shown by Reynolds et al. [Phys. Rev. B 40, 6210 (1989)].